Sparse graph-regularized dictionary learning for full waveform inversion

Full waveform inversion is a nonlinear fitting technique that requires regularization methods to alleviate ill-posedness. Based on the newly introduced Graph-Laplacian regularization, which offers outstanding manifold learning, we propose a novel regularization method for FWI that can combine the graph Laplacian matrix with a sparse representation in a learning-based dictionaries. Besides employing an adaptive sparsity prior, the graph Laplacian matrix incorporates the nonlocal self-similarity prior into the FWI process, and consequently improve the stability of the inversion process and produce more accurate inversion results. The Alternating Direction Method of Multipliers (ADMM) is applied to solve the problem numerically. A series of experiments are performed on the Marmousi model and the BG Compass model. The experimental results verify the effectiveness of the proposed FWI method in both quantitative analysis and visual perception.